G'day Jofm5,
The 'packs' refered to are the airconditioning units usually called packs. The B747 has three of them situated in the belly of the aeroplane. They are aircycle machines and use bleed air from the engines for their operation thus draining some power from them.
Completing a 'packs off' takeoff allows the engines to develop full rated thrust which will give a performance benefit in a limiting situation such as at hot and high elevation airports or at high gross weights.
Sometimes the APU can be used to supply the bleed air and run a pack or packs for takeoff, in any case once the immediate performance requirements have been met normal pack operation is restored.
Regards,
BH.